Ab-Initio Calculations of Nonlinear Susceptibility and Multi-Phonon Mixing Processes in a 2D Electron Gas Coupled to a Piezoelectric Material

Phonons promise to serve as an intriguing platform for technologies ranging from quantum computation to bioimaging. Particularly, compared to photons, phonon-based systems yield benefits ranging from vastly greater scalability to vastly reduced loss. A key challenge in harnessing phonons is inducing nonlinear interactions between them. To this end, we propose a heterostructure consisting of a piezoelectric material with a two-dimensional electron gas (2DEG) stacked on top. The piezoelectric material carries phonons in the form of surface acoustic waves. Due to the piezoelectric property of the material, each phonon also carries a quasi-static electric field, which extends into the 2DEG. The field induces polarization of 2DEG electrons, which in turn interacts with electric fields associated with other phonons. The net result is coupling between the various phonon modes. Here, we derive the nonlinear (second- and third-order) susceptibilities of a piezo-2DEG system with respect to quasi-static electric fields using analytical and numerical methods. In parallel, we derive the electric field per phonon as a function of the properties of the piezoelectric material and the 2DEG. Merging the susceptibilities and the electric field per phonon, we calculate the multi-phonon mixing dynamics. The results demonstrate a large acoustic nonlinearity in the system, paving the way to breakthrough technological applications.